Passivity of switched linear systems: Analysis and control design

• Published in: Systems & control letters Vol. 61; no. 4; pp. 549 - 554
• Main Authors: Geromel, José C., Colaneri, Patrizio, Bolzern, Paolo
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.04.2012; Elsevier
• Subjects: Applied sciences; Circuits; Computer science; control theory; systems; Control system synthesis; Control systems; Control theory. Systems; Design engineering; Disturbances; Dwell-time; Exact sciences and technology; Linear systems; LMI conditions; Passivity; Strategy; Switched systems; Switching; System theory; Switched systems; LMI conditions; Passivity; Dwell-time; Multimodel control; Stopping time; Time frequency domain method; Switching function; Feedback regulation; Control synthesis; Real positive function; Frequency domain method; Continuous time; Linear time; Passive system; Positive system; Linear control; Hybrid system; Time dependence; Linear time invariant system; Time domain method; Linear matrix inequality; State dependence
• ISSN: 0167-6911; 1872-7956
• DOI: 10.1016/j.sysconle.2012.02.008

A passive system with positive definite storage function is not only stable but is intrinsically robustly stable with respect to a wide class of feedback disturbances. For linear time invariant systems, passivity can be characterized either in time domain or in frequency domain from positive realness. This paper aims to generalize this concept to continuous-time switched linear systems. Analysis is performed by taking into account state dependent and arbitrary time dependent switching functions with a prescribed dwell time. A control design problem related to the determination of a switching strategy, based upon output measurements, that renders a switched linear system passive is also considered. The methods introduced in the paper can be effectively applied to the control of the duty cycle and passivation of switched circuits.